Can I fix the alpha display problems on material viewport on new Blender 2.73?
Do I need to worry about this on viewport?


No, I don't think so. The external game engine will be using it's own rendering pipeline, so any problems with the rendering then will be a separate and unrelated issue (with the possible exception of a problem with the data itself, e.g. double faces resulting in Z fighting etc. However this doesn't seem like the case here).


  Is there a way to fix it?


Try enabling Transparent in Properties > Object > Display on all the objects with transparency.